Data representation and data analysis can provide invaluable information within various disciplines of study. While various approaches to represent and analyze data exist, tree models, such as, additive trees, have become one way to represent and analyze data. The additive tree may correspond to a tree in which a non-negative weight may be attached to each link. A distance between two nodes of the additive tree may be defined as a sum of the weights assigned to the links constituting a path that connects the two nodes. Additive tree distances may satisfy the so-called additive inequality or four point condition.
However, in many types of clustering techniques, errors may exist. For example, decision errors may cause more clusters or fewer clusters to be present as compared to a number of clusters that actually exist in the data. To address these issues, cluster validation procedures may be implemented.